To find the total cost for purchasing \( x \) cartridges, you need to account for both the cost of the cartridges and the flat shipping fee.
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The cost of the cartridges: Since each cartridge costs $19, the total cost for \( x \) cartridges would be: \[ 19x \]
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The flat shipping fee: This cost is $7.50, which is a constant amount added regardless of the number of cartridges purchased.
Now, combine the cost of the cartridges with the flat shipping fee to form the total cost expression:
\[ \text{Total Cost} = 19x + 7.50 \]
So, the algebraic expression that describes the total cost for a single order of \( x \) cartridges is:
\[ 19x + 7.50 \]